Non-adiabatic Majorana brading protocol in a Y-shaped nanowire

Braiding of Majorana fermions is the primary logical operation of a topological quantum computer. Recently adiabatic Majorana braiding has been studied numerically for a realistic Y-shaped nanowire junction. In this work, we find optimized nonadiabatic braiding protocols on these Y junctions using simulated annealing and Pontryagin's minimum principle. These finite-time optimal protocols provide an advantage over the adiabatic evolution while preserving topological protection.